Problem: Rewrite as a simplified fraction. ${0.5\overline{91} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 591.9191...\\ 10x &= 5.9191...\end{align*}}$ Subtracting the two equations, we have: ${990x = 586}$ ${x = \dfrac{586}{990}} $ ${x = \dfrac{293}{495}} $